Third-order structure functions for isotropic turbulence with bidirectional energy transfer

Jin Han Xie, Oliver Bühler

Research output: Contribution to journalArticlepeer-review


We derive and test a new heuristic theory for third-order structure functions that resolves the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally, for example, in rotating stratified turbulence or magnetohydrodynamical (MHD) turbulence. The theory has three parameters - namely the upscale/downscale energy transfer rates and the forcing scale - and it includes the classic inertial-range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full range of data, therefore it has broader applications compared with the local theories, especially in situations where the data is imperfect. In addition, because of the resolution of forcing scales, the new theory can detect the scales of energy input, which was impossible before. We test our new theory with a two-dimensional simulation of MHD turbulence.

Original languageEnglish (US)
Article numberR3
JournalJournal of Fluid Mechanics
StatePublished - Oct 25 2019


  • MHD turbulence
  • isotropic turbulence
  • turbulence theory

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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